LEADER 05200nam 22007335 450 001 9910300255603321 005 20200630172554.0 010 $a1-4939-2969-0 024 7 $a10.1007/978-1-4939-2969-6 035 $a(CKB)3710000000521675 035 $a(SSID)ssj0001584977 035 $a(PQKBManifestationID)16262949 035 $a(PQKBTitleCode)TC0001584977 035 $a(PQKBWorkID)14864591 035 $a(PQKB)11026322 035 $a(DE-He213)978-1-4939-2969-6 035 $a(MiAaPQ)EBC5596144 035 $a(PPN)19053205X 035 $a(EXLCZ)993710000000521675 100 $a20151114d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aComputing the Continuous Discretely $eInteger-Point Enumeration in Polyhedra /$fby Matthias Beck, Sinai Robins 205 $a2nd ed. 2015. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2015. 215 $a1 online resource (XX, 285 p. 54 illus., 1 illus. in color.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-4939-2968-2 320 $aIncludes bibliographical references (pages 267-277) and index. 327 $aThe Coin-Exchange Problem of Frobenius -- A Gallery of Discrete Volumes -- Counting Lattice Points in Polytopes: The Ehrhart Theory -- Reciprocity -- Face Numbers and the Dehn?Sommerville Relations in Ehrhartian Terms -- Magic Squares -- Finite Fourier Analysis -- Dedekind Sums -- Zonotopes -- h-Polynomials and h*-Polynomials -- The Decomposition of a Polytope Into Its Cones -- Euler?Maclaurin Summation in Rd -- Solid Angles -- A Discrete Version of Green's Theorem Using Elliptic Functions. 330 $aThis richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart?s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler?Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: ?You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.? ? MAA Reviews ?The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.? ? Zentralblatt MATH ?This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.? ? Mathematical Reviews ?Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.? ? CHOICE. 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aCombinatorics 606 $aNumber theory 606 $aConvex geometry  606 $aDiscrete geometry 606 $aComputer mathematics 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aConvex and Discrete Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21014 606 $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026 615 0$aCombinatorics. 615 0$aNumber theory. 615 0$aConvex geometry . 615 0$aDiscrete geometry. 615 0$aComputer mathematics. 615 14$aCombinatorics. 615 24$aNumber Theory. 615 24$aConvex and Discrete Geometry. 615 24$aComputational Science and Engineering. 676 $a516.11 700 $aBeck$b Matthias$4aut$4http://id.loc.gov/vocabulary/relators/aut$0299625 702 $aRobins$b Sinai$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300255603321 996 $aComputing the Continuous Discretely$92536262 997 $aUNINA